Numerical simulations of combustion near solid and hydrogen permeable walls

P ra sh a n t S . S a lim a th D o ct o ra l t h e se s a t N T N U , 2 0 2 1 :3 0 6

ISBN 978-82-326-6568-6 (printed ver.) ISBN 978-82-326-6770-3 (electronic ver.) ISSN 1503-8181 (printed ver.) ISSN 2703-8084 (electronic ver.)

D o ct o ra l t h e si s Doctoral theses at NTNU, 2021:306

Prashant S. Salimath

Numerical simulations of combustion near solid and hydrogen permeable walls

N T N U N o rw e g ia n U n iv e rs it y o f S ci e n ce a n d T e ch n o lo g y T h e si s fo r th e d e g re e o f P h il o so p h ia e D o ct o r F a cu lt y o f E n g in e e ri n g D e p a rt m e n t o f E n e rg y a n d P ro ce ss E n g in e e ri n g

Numerical simulations of combustion near solid and hydrogen permeable walls

Thesis for the degree of Philosophiae Doctor Trondheim, 23rd of Sept 2021

Norwegian University of Science and Technology Faculty of Engineering

Department of Energy and Process Engineering

Prashant S. Salimath

NTNU

Norwegian University of Science and Technology Thesis for the degree of Philosophiae Doctor

Faculty of Engineering

Department of Energy and Process Engineering

© Prashant S. Salimath

ISBN 978-82-326-6568-6 (printed ver.) ISBN 978-82-326-6770-3 (electronic ver.) ISSN 1503-8181 (printed ver.)

ISSN 2703-8084 (electronic ver.) Doctoral theses at NTNU, 2021:306

Printed by Skipnes Kommunikasjon AS

NO - 1598

Dedicated to my parents, my wife Spurti and my daughter Manya.

”Time passes unhindered. When we make mistakes, we cannot turn the clock back and try again. All we can do is use the present well.”

- His Holiness Dalai Lama, 14th Dalai Lama of Tibetan Buddhism.

Abstract

The goal of the present thesis was to investigate a selective and isothermal, chemically inert hydrogen-permeable or porous wall boundary condition to laminar flame simulations to understand the flow physics of near-wall flames.

It provides better physical insight into a flame quenching process near a hydrogen-permeable wall, its relation to wall heat fluxes and incomplete combustion leading to pollutant formation. The simulation results are cru- cial to obtain prediction capabilities for eventual future utilization as novel fuel diffuser in a conventional combustor fuel nozzle. The comparison of the impermeable wall results with permeable wall results gives a good in- dicator towards building fuel diffuser and identifying a margin of operating conditions for improving hardware lifetime.

First, transient processes of laminar flame-wall interaction and quench- ing near a porous, permeable wall were investigated for the temperature of 750 K. These results were compared against a reference case of a non-porous or solid wall. The results obtained for lean, stoichiometric and rich initial mixture conditions in premixed flame show that flame wall characteristics (wall heat flux and quenching distance) are affected by the flux of hydrogen gas through a porous wall. The presence of a feedback mechanism was ob- served between hydrogen flux at wall and flame, which influences boundary layer flashback speeds in 2-d side wall quenching (SWQ) cases. The strong feedback effect was observed at lean-fuel conditions.

Then, a laminar 1-d head-on quenching (HOQ) of hydrogen-air mixture for the permeable wall was extended to study the effects of varying wall mass flux, stoichiometry, inert dilution and unburned-gas and wall temperatures.

In all cases, the maximum reaction heat release rate occurred at the wall.

For rich and stoichiometric mixtures, a moderate reduction of the quenching

(i.e.maximum) wall heat flux to permeable wall in comparison to reference

impermeable wall, whereas for a lean mixture, the increase of quenching wall

heat flux was considerable. The lean permeable wall cases have similarities

to much richer impermeable wall cases. Both a lower wall temperature and

dilution reduce the burned-mixture temperature and, consequently, the wall

heat flux.

Furthermore, the flame wall interaction study with a hydrogen-permeable wall was extended to methane-air premixed flames. Permeable wall (PW) configurations were investigated for two temperatures at 600 and 750 K, of the wall and unburnt gas, and varying initial equivalence ratios. The solid wall results agreed with previous FWI studies. The mutual effects of convection heat transfer, flame behaviour and local fuel-air ratio, with re- duced temperature and heat release rates, explain the flame quench before reaching the wall for PW cases. These effects were not observed for FWI of premixed hydrogen-air mixtures. The quenching definition of maximum heat flux was inappropriate to these cases. The OH radicals concentration was taken as a criterion for quenching definition and flame position.

Finally, the interaction of premixed hydrogen-air flame was extended to study local entropy generation and entropy fluxes towards a solid and hydrogen-permeable wall. Major findings were that conduction entropy generation remains dominant close to quenching, and that fuel permeation through the wall tends to reduce entropy generation per unit of converted fuel, particularly for initially lean mixtures.

v

Preface

This thesis is submitted to the Norwegian University of Science and Tech- nology (NTNU) for partial fulfillment of the requirements for the degree of philosophiae doctor. This doctoral work has been performed at the De- partment of Energy and Process Engineering, NTNU, Trondheim, with Ivar S. Ertesv˚ ag as main supervisor and Andrea Gruber as co-supervisor. The present work is conducted at NTNU, in close collaboration with SINTEF Energy Research.

This work is part of combustion under NTNU project CCERT (CO

Capture with Enabling Research and Technology), funded by the Research

Council of Norway, Det Norske Veritas AS, Shell Technology Norway AS,

StatOil Hydro AS and Metso Power OY.

Acknowledgements

I would like to express my deepest regards to my supervisor, Professor Ivar S. Ertesv˚ ag, for trusting me to pursue my own ideas and thoughts, and for his continuous interest and support. Special thanks to Dr. Andrea Gruber for his valuable support in understanding of S3D code, fruitful discussions and inspiring enthusiasm. A very special thanks to Prof. Inge Gran, for initial years of supervising my work.

I am pleased to express my acknowledgement to Dr. Andrea Gruber for his co-operation and possibility on implementation of permeable wall boundary in S3D code. Many thanks to all my colleagues at Department of Energy and Process Engineering at NTNU.

Notur/The Norwegian e-infrastructure for Research and Education, Uni- nett Sigma, has provided the computational resources for the simulations (project No. nn9400k). Their HPC support team is thanked for all help and support in running the simulations. Special thanks to the supporting staff from IT department for their help and support with different IT issues.

Finally, my family also deserves special thanks for their support and

understanding during these years of study.

Papers and Presentations

The thesis is based on following research articles.

Article 1. Andrea Gruber, Prashant S. Salimath and Jacqueline H.Chen, 2013, Direct Numerical simulation of 1-D and 2-D laminar flame-wall inter- action for a novel H

-selective membrane/injector configuration. Interna- tional Journal of Hydrogen Energy, 39, 5906-5918.

Article 2. Prashant S. Salimath, Ivar S. Ertesv˚ ag and Andrea Gruber, 2018, Premixed hydrogen flames interacting with a hydrogen porous wall.

International Journal of Hydrogen Energy, 43, 3822-3836.

Article 3. Prashant S. Salimath, Ivar S. Ertesv˚ ag and Andrea Gruber, 2020, Computational analysis of premixed methane-air flame interacting with a solid wall or a hydrogen porous wall. Fuel, 272, 0016-2361.

Article 4. Prashant S. Salimath and Ivar S. Ertesv˚ ag, 2020, Local entropy generation and entropy fluxes of a transient flame during head-on quenching towards solid and hydrogen-permeable porous walls. International Journal of Hydrogen Energy, 46, 22616-26630.

Ivar S. Ertesv˚ ag and Andrea Gruber are my main supervisor and co- supervisor, respectively.

Author’s Contribution

The papers are co-authored. The author of the thesis has contributed to research work in the following :

Paper 1. The first author (Andrea Gruber) formulated the theoretical for- malism of the permeable wall boundary conditions (BCs) while the second author (Prashant Salimath) conducted the first numerical implementation and testing of the BC in the S3D code. Further and final implementation of permeable wall BC in S3D was done by first author. The main contribution by second author to the article was on performing some of the numerical 1-d

viii

DNS presented in the paper. The first author conceived an idea on flame back for 2-d SWQ (side-wall quenching) and performed 2-d DNS results in the paper and was responsible for writing the article with the interpre- tation of the results and discussion. The third author (Jacqueline Chen) contributed with suggestions and critical reviews.

Paper 2. The first author (Prashant Salimath) conducted all the numeri- cal simulations of 1-d HOQ (head-on quenching) for the impermeable and hydrogen-permeable walls with design parameter variations (feed pressures, wall temperatures, equivalence ratios and dilution effects). The first author wrote the paper with the interpretation of the results and discussion. The second author (Ivar S. Ertesv˚ ag) supervised the writing and article layout through discussions and suggestions. The third author (Andrea Gruber) contributed with critical reviews.

Paper 3. The first author (Prashant Salimath) conceived the idea of simula- tions of 1-d HOQ for methane flames with hydrogen permeable wall condi- tion. The first author did all the numerical simulations and wrote the paper with the interpretation and discussion of the results. The second author (Ivar S. Ertesv˚ ag) supervised the writing and article layout through discus- sions and suggestions. The third author (Andrea Gruber) contributed with critical reviews.

Paper 4. The first author (Prashant Salimath) conceived the idea of comput- ing local entropy generation in 1-d HOQ for hydrogen flames with hydrogen permeable wall. The author also performed all numerical computations.

The second author (Ivar S. Ertesv˚ ag) was responsible for writing the pa- per with the interpretation and discussion of the results. The first author arranged numerical results in the article based on discussions, suggestions and critical reviews given by the second author.

ix

Nomenclature

Acronyms

DNS Direct Numerical Simulation FWI Flame-wall Interaction HOQ Head on Quenching IW Impermeable or Solid wall PW Permeable Wall

RHS Right-hand side SWQ Side Wall Quenching Greek Symbols

λ thermal conductivity J/(s·m·K)

µ viscosity Pa·s

φ equivalence ratio −

ρ mass density kg/m

τ

viscous stress tensor Pa

Latin Symbols

C

,C

specific heat capacity at constant pressure (for species i) J/(kg·K) D

mixture-averaged mass diffusivity of species i m

/s D

thermal diffusion coefficient of species i kg/(m·s)

F

wall flux for species i kg/(s·m

)

h

specific enthalpy for species i J/kg

J

diffusive mass flux of species i in x

direction kg/(s·m

) L

,L

spatial dimensions for axial and transverse direction m

n pressure exponent −

N

number of spatial dimensions −

N

number of species −

p, p

pressure, reference pressure Pa

P e

Peclet number −

Q

hydrogen membrane permeance kmol/(m·s·Pa

)

q

heat flux in x

direction J/(s·m

)

R specific gas constant for the mixture J/(kg·K)

x

S

laminar flame speed m/s

t time s

T , T

temperature, ambient temperature K

U primitive variables solution vector −

u

velocity component in x

direction m/s

W

molar mass of species i kg/kmol

x, x

spatial coordinate m

x

, y

non-dimensional axial and transverse direction −

y spatial coordinate m

Y

mass fraction of species i −

Superscripts

f hydrogen pressure on feed side p hydrogen pressure on permeate side Subscripts

α, β directional indices

b property of the burnt mixture u property of the unburnt mixture w wall quantity

xi

Contents

Abstract iv

Preface vi

Acknowledgements vii

Papers and Presentations viii

Contents xiii

1 Introduction 1

1.1 Background and motivation . . . . 1

1.2 Objectives and research questions . . . . 6

1.3 The S3D code for computational fluid dynamics . . . . 8

1.4 Research Strategy and report layout . . . . 10

2 Models, boundary conditions and numerical methods 13 2.1 Mathematical models . . . . 13

2.2 Boundary conditions . . . . 14

2.2.1 Well-posed boundary conditions . . . . 14

2.2.2 Closed (wall) boundary conditions . . . . 15

2.3 Numerical methods . . . . 17

3 Summary of articles 18 3.1 Schematic outline . . . . 18

3.1.1 Article 1 . . . . 20

3.1.2 Article 2 . . . . 21

3.1.3 Article 3 . . . . 22

3.1.4 Article 4 . . . . 23

3.2 2-D side-wall quenching (SWQ) configuration . . . . 24

3.3 Discussion . . . . 28

xii

4 Conclusions and further work 31 4.1 Summary . . . . 31 4.2 Future work . . . . 33

Bibliography 42

Appendices 43

A Selected Papers . . . . 44 B Chemical kinetics mechanism . . . 108

xiii

xiv

Chapter 1

Introduction

1.1 Background and motivation

Human civilization has witnessed significant progress and development by the discovery of fire [1]. The controlled fire application as energy source made remarkable progress in human society in terms of historical pieces of evidence suggests that ancestors improved their food habits that eventually improved brain size and thinking abilities [2, 3]. Traditionally, fire has been used in various forms for heating, illumination and advanced craftsmanship, such as the development of metals [4, 5]. But as evolution progressed with time, the fire seemed to be an inadequate energy source, and alternative energy sources derived from fossil fuels were sought to meet growing en- ergy demand. Nowadays, global energy figures indicate major concerns of by-products of combustion, leading to pollution, which has long-term en- vironmental impact [6]. However, the availability of fossil fuels remains by a far major source of energy [7]. An increasing world population and fast pace development of third world countries led to a steep rise of the energy demand [8, 9]. The increase in energy demand began to grow further with the industrial revolution from the 18th century [10]. Until the end of the 19th century, energy demand was met by conventional fuels such as wood, charcoal and coal.

1

The discovery of oil and natural gas resources, significantly changed the dynamics of energy demand in the modern world [11]. The International Energy Agency (IEA) estimated that global energy consumption (including fossil fuels, renewable, nuclear and bio fuels) grew by 2.3% worldwide in 2018, which is near twice the average growth rate since 2010. The global energy consumption is largely driven by a robust economy and also higher heating and cooling needs in some parts of the world. The latter lead to an increase of the CO

emissions to 33.1 giga-tonnes from 2010 to 2018, which is equal to 1.7% [8]. The coal-fired power generation remains to be the single largest emitter, accounting for 30% of all energy-related carbon dioxide emissions. This results to an increase of emissions due to the release of local and global pollutants [12]. The rising energy demand trend in World Energy Outlook (WEO) suggest a 37% increase in coming 2040 as compared to 2014 [8]. WEO indicated that developed countries are stable in energy demand. In contrast, developing countries with a huge population, such as China and India, show unexpected higher energy demand in coming years [8]. Also, calculation suggests that fossil fuel reserves of oil and gas can last till 2042 and coal reserves are available up to 2112, according to Shafiee and Topal [13]. In the coming 20 years, current technology may not be relevant as oil and gas as a primary energy source may get exhausted.

Alternative renewable energies are looked upon to reduce the dependency on fossil fuels. However, in the recent years they still did not provide an attractive option to replace fossil fuels. It is predicted that dominant energy sources will still be based on oil, gas, coal and low-carbon sources, with little change in their share of total consumption [14]. The effective campaign to reduce dependency on fossil fuels and greenhouse gas emissions has not been stringent across the world. The 1997 Kyoto protocol and its signatories have not fulfilled the commitments towards reducing greenhouse emissions [15].

Although various efforts have made to reduce fossil fuels dependence by 25% to current available technologies available, it may not be enough to reduce the global greenhouse effects. If emissions continue to increase at the current rate, the atmosphere will warm up by 1.5 degrees Celsius above pre-industrial levels by 2040 [16]. The consequences are coastlines flooding

2

and exacerbation of droughts and poverty.

It is becoming an alarming issue to attenuate temperature increase to below 2 degrees Celsius and less than 1000 giga-tonnes of CO

emissions to avoid climatic changes and natural calamities. From 2014, various organizations such as Advisory Council for Aviation Research and Innovation in Europe (ACARE) set in with stricter norms on emissions to mitigate 20% of CO

and NOx by 80% per passenger [17].

In the present-day situation, available energy fuel sources produce green- house gas emissions. There have been significant efforts put into large scale implementation of carbon capture and storage (CCS) technologies to re- duce fossil-based CO

emissions. CCS is considered a crucial strategy for meeting CO

reduction targets for fossil fuels [18, 19, 20]. Most studies concluded that the costs of pre-combustion CO

capture from syngas in an integrated gasification combined cycle (IGCC) plant were much lower than post-combustion removal from pulverized coal (PC) or natural gas combined cycle (NGCC) plants [21, 22, 23]. One of the common strategies employed in stationary gas turbine power generation is to opt for pre-treatment of natural gas fuel, as it contains mainly methane gas. The methane gas is reformed to a syngas containing H

and CO [24]. The hydrogen content can be increased by the water-gas shift reaction with low CO gas content.

However, the downside of considering the pre-combustion CCS technologies as an option, is that it adds costs to process, which comes from the procure- ment of reforming and H

separation units [25]. Current technology con- cepts available use the auto-thermal reforming (ATR) with water-gas shift reaction reactors to produce hydrogen-rich syngas from natural gas, and CO

produced is separated further by adsorption [26]. There is one poten- tially more efficient alternative introduced of hydrogen transport membrane (HTM) [27]. In HTM, water shift reaction and hydrogen separation from CO

are combined in the same unit [28, 29]. The hydrogen gas produced is further utilized as a fuel source mixed with compressed inert diluent, i.e.

nitrogen, for the burner. The addition of diluent reduces the reactivity of hydrogen as it flows out of the fuel injection nozzles and mixes with the

3

compressed hot air. In the pre-mixed burner, the diluent provides flashback safety for reactive H

fuel.

Industrial gas turbines commonly utilize lean pre-mixed burners for NO

control using low reactivity fuels, such as natural gas [30]. These conven- tional gas-fuel injector nozzles usually operate in a transverse-jet configu- ration, where fuel exiting the nozzle mixes with approaching oxidant at an angle that is approximately normal to the oxidant flow [31]. However, al- though transverse-jet nozzles typically achieve good flow penetration and mixing of the fuel in the oxidant flow, they also result in a low-velocity flow region on the leeward side of the jet. This is especially problematic in the case of the highly-reactive hydrogen fuel due to the possibility of flame attachment directly at the nozzle exit and lack of intrinsic flashback resis- tance (the flame is flushed downstream once the instability that displaced it upstream recedes).

Lean pre-mixed burners were originally designed for natural gas applica- tions. Subjecting burners to a modification to accommodate more reactive fuels, such as hydrogen, leads to significant design challenges for achieving acceptable flame stability. The technical difficulties of burner handling re- active fuel are to avoid the occurrence of (a) flame flashback, an undesired event of upstream flame propagation in the premixed section of the burner and along the wall surfaces of the nozzle due to aerodynamic effects [32], and (b) stable flame anchoring near-wall surface of injection nozzles due to the presence of local fuel-rich conditions [33, 34].

In the present study, a novel burner concept development is envisaged as shown in Fig. 1.1 for a stationary gas turbine that operates as a porous diffuser coated with an H

selective membrane that can operate in a lean premixed mode. The porous fuel diffuser has the potential to replace con- ventional gaseous fuel nozzles with holes for injection, thereby avoiding point fuel sources of highly reactive H

fuel. In the porous diffuser, an H

flux can be supplied based on the high pressure difference between feed and per- meate side of the membrane leading to a uniform diffusion of the fuel. The porous ceramic or steel can act as opportunely shaped diffusers. A recent

4

experimental study investigated the effects on premixed flame shape and stabilization of a novel approach for spatially distributed reactive hydro- gen fuel injection through a porous steel surface integrated into the burner design [35]. However, great care must be taken in designing primary air flow interacting with a permeable wall surface to quickly remove reactive H

from the near wall region to avoid flashback of the flame and flame an- choring near the immediate vicinity of fuel injection. Other construction details of the novel burner are left out in the scope of present work and are not discussed.

Figure 1.1: Fuel injector sketch with in-situ separation of hydrogen gas from syngas. Adapted from Article 1.

Figure 1.2: Head-on quenching configurations of (a) Impermeable wall (IW) and (b) Permeable wall (PW) with hydrogen flux. Premixed fuel can be hydrogen or methane gas.

5

Figure 1.3: Side-wall quenching configurations of (a) Impermeable wall (IW) and (b) Permeable wall (PW) with hydrogen flux. Premixed fuel can be hydrogen or methane gas.

1.2 Objectives and research questions

Combustion near a high-temperature membrane surface with the fuel sup- ply has the important feature of lowering the partial pressure of species con- sumed in the combustion process, leading to a larger driving force across the membrane. The use of membranes opens for novel applications in porous fuel nozzle design in gas turbine development such as nano or micro com- bustion, where wall effects are significant.

The primary aim of the work is to improve the understanding of combustion close to a porous wall. Novel designs demand particular attention to flame- wall interaction processes to understand combustion inefficiencies such as poor mixing, incomplete combustion and high wall heat flux. The main focus of the investigations will be laminar flame-wall interactions (FWI) of premixed flames with the PW in the head-on quenching (HOQ) configura- tions (Fig. 1.2) for laminar premixed flames of hydrogen-air and methane- air mixtures. This study will provide better estimates of wall heat flux characteristics and H

fluxes for operating conditions for varying fuel-air conditions, wall temperatures and diluents effects. In FWI simulations, no previous reports or literature were available on hydrogen-PW simulations.

The results will be compared against reference IW cases as both walls are

6

will be kept isothermal and chemically inert. Laminar side-wall quenching (SWQ) as shown in Fig. 1.3 was performed to assess boundary layer flash- back resulting from the feedback mechanism between membrane hydrogen flux and the propagating flame for hydrogen-air mixture.

The following research questions were addressed in the articles:

• How does PW influence near-wall flame behaviour and flame quench- ing characteristics compared to IW in hydrogen-air mixtures? How do design parameter variations affect flames during the flame quenching process in PW hydrogen-air flames?

It can be anticipated that hydrogen permeation through a PW will influence the flame behaviour and change the characteristics compared to IW. Article 1 will investigate some aspects of 1-d and 2-d cases, while Article 2 will extend the 1-d study at different stoichiometries with varying permeation pressure (wall mass flux), unburnt and wall temperature, and dilution of the hydrogen-air mixture.

• How does hydrogen wall permeation into a methane-air mixture affect the near-wall flame behaviour and head-on quenching characteristics?

In Article 3, hydrogen PW injection into methane-air will be investi- gated and compared to the corresponding IW cases.

• How does fuel permeation through the wall influence entropy genera- tion in the transient flame quenching process ?

The entropy generation expresses the thermodynamic losses in the process and is important for energy conversion optimization. Article 4 will investigate the entropy generation for PW and IW cases from Article 2.

7

1.3 The S3D code for computational fluid dynamics

In the present work, implementation of wall boundary condition with se- lective hydrogen species permeability was performed in the S3D code. The permeable-wall (PW) boundary condition implementation is based on Siev- erts’ law of diffusion [27]. The numerical simulations were performed in S3D using high-order finite-difference stencils and numerics [36].

S3D is a Fortran-based direct numerical simulation (DNS) code. It was de- veloped under a research program of the United States Department of En- ergy (DoE) at the Combustion Research Facility (Livermore, CA). The code is programmed in Fortran F77/F90 code that uses message passing interface (MPI) for inter-process communication in parallel execution. The code is portable to different platforms /architectures including Linux clustres, IBM SP, Windows PC, Cray DEC, SGI Origin and DEC Alpha clustres. This code has been successfully used previously for a range of studies, including non-premixed flames [31, 33, 34, 37], premixed flames [38, 39, 40, 41, 42]

and autoignition [43, 44].

Fig. 1.4 displays a flow diagram of S3D. The structural procedures are de- scribed in this section [45, 46]. The implemented algorithm solves compress- ible Navier-Stokes equations in the conservative form on a structured grid mesh in 1, 2 or 3 spatial directions. The structured code runs in either an execute-in-the-run mode (’0’) or a post-processing mode (’1’). However, the post-processing mode can run only when time sampling data are available from prior run-mode simulations.

The code integrates the governing equations in run mode forward in time.

All necessary operations are directed by routine solve driver code for a case- specific initialization of the primitive variables. After the initialization of the primitive variables, three components of transport equations convective, diffusive and source terms update for each time step in the conservation equations by high order time advancement solver of Runge-Kutta scheme [47]. In post-processing mode, the code executes with the same processor topology as in the run mode, but all required operations are directed by

8

the post-driver routine. The main kernels for solver accounts for 95% of the computation.

The following is a list of main kernels given below:

• Chemistry module: This module computes source terms of species transport equations that are chemical reaction rates. The ”getrates”

code, generated by the Chemkin compatible utility auto-getrates pack- age, preprocesses the chemical kinetics data and computes reaction rates. A separate module is built for routines to be packaged and interfaced to the S3D code. This module abstracts the actual imple- mentation of the reaction rates computation, and it also offers flexi- bility to use different versions of the getrates subroutine targeted at different platforms.

• Transport module: This module computes species molecular transport properties. Transport properties include viscosity, thermal diffusivity and species mass diffusivities. The chemical reactions and transport coefficients are calculated from CHEMKIN and TRANSPORT pack- ages respectively [48]. The scalar transport properties are approxi- mated with a constant Lewis number for each species or referred to as mixture averaged properties. Soret effect or thermo-diffusion and pres- sure diffusion terms are included, but the Dufour effect is neglected.

• Thermodynamics module: Computes thermodynamic properties that include species enthalpy and specific heats of the mixture. Thermo- dynamic data are provided to Chemkin compatible format. The pre- processing of data is performed through the chemkin interpreter. The evaluation of properties using the chemkin routines, the code employs a tabulation and lookup strategy.

• Derivatives module: This module computes spatial derivatives of the primitive variables from conserved variables. It uses high-order finite- difference operators of eighth order, A finite difference explicit scheme is used with tenth-order explicit spatial filter ([49]) to remove spurious

9

high-frequency noise and mitigate aliasing error. The code uses non- blocking sends and receives to exchange the data at the processor boundaries among different processors.

• Other RHS module: Fig. 1.5 shows right-hand side (RHS) of the time advance equation which involves all of the operations mentioned above and the convection terms. These terms summed up, and operations involved in this procedure are lumped into the RHS module for ac- counting purposes.

• Time Integration module: It advances the solution in time using a six-stage, fourth-order explicit Runge-Kutta scheme [47]. This mod- ule also includes an error controller, which routinely checks through proportional-integral-derivative (PID) to achieve optimal time steps and time accuracy of the solution with desired error tolerances.

More details on chemical source terms and thermodynamics and equations description can be found in [36] and Articles 2 and 3.

The present simulations were performed in the Vilje cluster. This clus- ter belongs to the Norwegian e-infrastructure for Research and Education, UNINETT Sigma2, which is funded by the Research Council of Norway, NTNU and the Universities of Oslo, Bergen and Tromsø. It offers a dis- tributed memory system that is well suited for large scale parallel MPI ap- plications. It consists of 1440 nodes interconnected with a high-bandwidth low-latency switch network (FDR Infiniband). Each node has two 8-core Intel Sandy Bridge (2.6 Ghz) and 32 GB memory. The total number of cores is 23040.

1.4 Research Strategy and report layout

The S3D DNS code is used to perform the transient simulations of lam- inar flame propagation towards the wall. The reactive flow is simulated, taking into account of thermo-physical properties. The detailed chemical

10

Figure 1.4: S3D code: Main program flow diagram.

kinetics is enabled to capture radical recombination reactions character- ized by low activation energies in near-wall region. It was observed that modelling of quenching process with single-step chemistry approximation in previous FWI studies led to considerable uncertainties in flame quenching characteristics, which could adversely influence to other physical quantities characterizing the flow [50, 51].

The flame interaction with ”cold” walls (< 400 K) results in water conden- sation effects are observed by [52]. This condensation of water can act as a possible reducing factor for wall heat flux. Also, wall temperatures above 400 K as ”hot” wall depend upon material type and can influence as a cat- alyst through radical absorption, desorption and recombination, which can play an important role in the flame-wall interaction processes. However, in the present simulations, wall surfaces are assumed as an chemically inert wall and an isothermal wall condition is maintained. Both water condensa- tion and surface kinetics are absent at the wall in the present study. This

11

Figure 1.5: S3D RHS module : Flow diagram.

makes the conclusions of results produced independent of any particular properties of the wall surface material.

In the permeable wall boundary, the permeability of reactive hydrogen gas depends upon partial pressure difference between feed and permeate side of the wall. High pressure at the feed side is maintained at a maximum of 10 atm as the largest value in present simulations, which ensures optimum hydrogen flow rates across the wall.

The mathematical background description of governing equations, wall bound- ary condition formulation and numerical methods are described in Chapter 2. Chapter 3 presents the summary and contribution as articles published, and Chapter 4 is the conclusion of research work, and further work is de- scribed. The appendix includes of the peer-reviewed published papers and the chemical kinetics mechanism of hydrogen-air and methane-air.

12

Chapter 2

Models, boundary conditions and numerical methods

For laminar FWI studies in S3D code, Navier-Stokes equations are solved for subsonic, reacting compressible flow conditions.

2.1 Mathematical models

The governing equations, thermodynamic and transport properties are de- scribed in each article and not repeated here.

Numerical integration of governing equations as a system of partial differ- ential equations gives the solution vector of conserved variables. Further, primitive variables solution vector is computed, U as :

U = (ρ, u

, p, T, Y

)

α = 1, 2, 3 i = 1, 2, · · · , N

(2.1)

13

2.2 Boundary conditions

The governing equations are a coupled system of non-linear partial differ- ential equations. Their solution for a specific flow configuration is strongly dependent upon the specification of boundary conditions at computational domain boundaries and initial conditions for all flow variables in the entire field.

2.2.1 Well-posed boundary conditions

In DNS, special care is required for the boundary conditions specification to meet objectives: (1) to represent the flow physics of the near-wall re- gion or nature of turbulent flow conditions, and (2) compatible with high- order numerical schemes for spatial and temporal discretization [53]. For well-posedness for solving fluid flow problem, boundary conditions are dis- tinguished into physical boundary conditions and artificial boundary con- ditions. The artificial boundary conditions are required to satisfy the well- posedness condition. Such boundary conditions are often difficult to for- mulate and act as complementary relations along with physical boundary conditions.

Table 2.1 lists boundary conditions required for well-posedness to solve Navier-Stokes equations and Euler (non-viscous) equations [54, 55, 56].

Table 2.1: Number of boundary conditions required well-posedness for the Euler and Navier-Stokes equations.

Flow type Euler Navier-Stokes

Supersonic inflow N

+ 2 + (N

- 1) N

+ 2 + (N

- 1) Sonic inflow N

+ 1 + (N

- 1) N

+ 2 + (N

- 1) Subsonic inflow N

+ 1 + (N

- 1) N

+ 2 + (N

- 1)

Subsonic outflow 1 N

+ 1 + (N

- 1)

Sonic outflow 0 N

+ 1 + (N

- 1)

Supersonic outflow 0 N

+ 1 + (N

- 1)

No flow 1 N

+ 1 + (N

- 1)

14

The physical boundaries are categorized into open and closed boundaries. In open boundaries, inflow and outflow boundary conditions are widely used in practical applications [57, 58, 59, 60]. The characteristic boundary condition (NSCBC) method is used to describe non-reflective pressure waves in open boundaries and represents an artificial cut through the flow field at both ends of the domain. In closed boundaries, there is no flow across the boundary, which represents wall condition in practical applications. The following section discusses boundary conditions treatment for wall boundaries. The radiative heat transfer is neglected in the wall boundary formulation.

2.2.2 Closed (wall) boundary conditions

In wall-bounded flows, wall boundaries play a dominant role in the FWI process. The presence of a wall boundary influences the local chemistry in the near-wall region, leading to a large wall heat release at quenching of the flame. In the following, wall formulations of an impermeable wall (IW) and a hydrogen permeable wall (PW) boundaries are discussed.

A number of N

+1 + (N

- 1) of physical boundary conditions are re- quired to satisfy well-posedness for an inert, isothermal, no-slip wall bound- ary. These conditions are applied to Navier-Stokes equations for a com- pressible gas mixture. One may write these as :

u

= 0, T

= T

, F

= 0 i = 1, 2, · · · , N

(2.2) The species flux condition satisfies impermeability condition for IW, where F

= 0 for all species i. For PW, F

= 0 except i = H

.

When applied to the momentum equation (with no body forces), the imme- diate consequences are for the IW formulation :

∂u

∂t = Du

Dt = 0,

∂p

∂x

w

= ∂τ

∂x , (2.3)

Numerical inversion of the pressure gradient expression, will yield the pres-

15

sure at the wall (p

). Similarly, the species mass fraction at the wall (Y

) are extracted by inverting the wall species gradient term.

With known values of p

, Y

and T

, the fluid density at wall node, ρ

is computed from the equation of state. In summary, this wall formulation is applicable for solid or IW boundary conditions. This formulation has been widely used in wall-bounded flow studies with the S3D code [31, 33, 34, 38, 39].

For the PW formulation, a selective H

species flux condition is limited by diffusion and is modelled by :

F

= W

Q

(p

2

)

− (p

2

)

(2.4) The re-arranged Fick’s law expression gives the species mass fraction gradi- ent at the wall and it is given as:

∂Y

∂x

w

= F

ρ

D

(2.5)

Note that all species except H

follow the species impermeability condition in Eq. 2.2.

Owing to species flux, the pressure at the wall is updated by re-arranging the momentum equation leading to:

∂p

∂x

w

= −

NS

X

i=1

∂F

∂t − ∂u

∂x

NS

X

i=1

F

+ ∂τ

∂x (2.6)

The first and second RHS terms represent the unsteady and steady contri- butions to the wall-normal momentum of the PW hydrogen flux. Here, u

is the non-zero wall-normal velocity component due to hydrogen permeation.

The new values of Y

and p

are extracted by inverting (numerically) Eq. 2.5 and Eq. 2.6, respectively. Then, density at the wall, ρ

can be computed from the equation of state.

16

2.3 Numerical methods

The high-order finite-difference schemes are employed in S3D code because of their lower computing costs than those of high-order finite-volume meth- ods [61, 62]. The high-order finite difference schemes including one-sided stencils for wall boundaries, filtering and temporal discretization details are discussed in [63] and are not repeated here.

17

Chapter 3

Summary of articles

The main contribution to research work is compiled into four papers which are submitted/published in peer-review journals.

3.1 Schematic outline

The author contributions are highlighted in Fig 3.1, and an overview of the key points in each article is summarised. Article 1 is a starting point with the implementation of PW boundary conditions in 1-d HOQ and 2-d SWQ configurations for understanding near-wall physics. It also offers forking paths (I and II) of FWI studies into Articles 2 and 3 for hydrogen-air and methane-air mixtures, respectively. Article 4 extends the Article 2 study with computations of entropy terms or irreversibilities during the transient flame quenching process.

18

Figure 3.1: Outline of the scientific articles

19

3.1.1 Article 1

Title : Direct numerical simulation of laminar flame–wall interaction for a novel H

selective membrane injector configuration.

Co-Authors: Andrea Gruber and Jacqueline H. Chen

In this paper, transient simulations of laminar flame-wall interaction and quenching near a porous, permeable membrane wall (PW) for 1-d HOQ and 2-d SWQ configurations are presented. The comparison of these results is conducted with the reference case of a non-porous impermeable wall con- dition. The simulations were performed using S3D DNS (Direct Numerical Simulation) code [36] with detailed chemkin kinetics of hydrogen-air com- bustion [64]. The main aim of the study to future utilization of porous metal surfaces (or porous fuel diffuser) as a fuel distributing source for H

injec- tion into the oxidant stream of a gas turbine burner. Also, understanding of near-wall flow physics of PW for highly-reactive hydrogen-rich fuels in the feed side. The PW wall boundary condition formulation is based on mod- elling selective species (hydrogen in this case) transport through a porous wall is discussed. The hydrogen flux of PW is driven by the partial pres- sure difference between the feed and the permeate side of the membrane.

The numerical results are performed for 3 cases: lean, stoichiometric and rich initial mixture conditions on the permeate side of the membrane. It was observed that FWI characteristic parameters (wall heat flux, quenching distance) are affected to a large extent by the presence of the membrane. It is shown that quenching wall heat flux is increased by a factor of three for the (initially) fuel-lean premixed flame 0.5 in the presence of PW compared to the standard IW case. The high wall heat flux is due to the higher flame temperature attained in the near-wall region immediately before quenching and to the presence, in the initial mixture, of excess oxygen that continues to burn in a secondary non-premixed flame after quenching of the primary premixed flame. The hydrogen flux through the membrane is also strongly affected by the presence of the flame during the transient flame-wall interac- tion process, finally resulting in a strong feedback effect between membrane and flame that greatly increases boundary layer flashback speeds at fuel-lean

20

conditions. The paper suggests to having carefully designed fuel diffuser to remove hydrogen rapidly near-wall region of the permeate side of PW and mixing with oxidant more uniformly to achieve target fuel-air mixture. This work provide a starting point for understanding the interaction of PW for 1-d HOQ for different design parameters, as discussed in article 2.

3.1.2 Article 2

Title : Premixed hydrogen-air flames interacting with a hydrogen porous wall.

Co-Authors: Ivar S. Ertesv˚ ag and Andrea Gruber

In this paper, a laminar 1-d hydrogen-air flame travelling and quenching towards a chemically inert permeable wall (PW) was studied for designed parameter variations (effects of varying wall mass flux, stoichiometry, inert dilution, and unburned gas and wall temperatures). H

as additional fuel seeped through the permeable wall into premixed H

-air mixtures based on partial pressure difference of feed and permeate side. All simulations were performed with detailed hydrogen-air chemistry in S3D code [36, 64]. These results are compared against the results of an impermeable wall (IW). All cases, maximum reaction heat release rates at the wall was observed. For rich and stoichiometric mixtures, PW with fuel influx gave a moderate re- duction of the quenching (i.e.maximum) wall heat flux compared to IW. In contrast, for a lean mixture, the increase is considerable. The fuel influx ef- fect on the importance of individual elementary reactions and radicals and intermediate species for rich and stoichiometric mixtures. The hydrogen permeation in PW led to locally richer flame (i.e. partially premixed mix- ture formation). It can be observed that more H radicals and less O radicals are present close to the wall and exothermic reaction recombining H to H

is considerably more important for PW. This consumption of H inhibits the more exothermic reaction of OH and H to H

O. This overall influence early wall effects with more distant from the wall than for IW. Both a lower initial temperature and dilution with H

(inert) or H

O (participating) reduce the

21

burned-mixture temperature and, consequently, the wall heat flux. Also, flame propagation and quenching are delayed.

3.1.3 Article 3

Title : Computational analysis of premixed methane-air flame interacting with a solid wall or a hydrogen porous wall

Co-Authors: Ivar S. Ertesv˚ ag and Andrea Gruber

The objective of the paper was an investigation of flame-wall interaction process for premixed methane-air flames by direct numerical simulation us- ing S3D code. Canonical configuration of 1-d HOQ with an isothermal, chemically inert impermeable wall (IW) and a hydrogen-permeable wall (PW) was taken with two temperatures of 600, and 750 K (of the wall and unburnt gas kept at the same temperature) were selected for the present study. Hydrogen released through the PW participated in the methane-air combustion as a secondary fuel.

For lean and stoichiometric mixtures, the reduced chemical mechanism of Smooke and Giovangigli (with slightly modified parameters) was used for simulations [65]. The mechanism does not include C2-chemistry but pro- duced satisfactory results. For rich methane-air mixtures, the DRM22 mech- anism was used that includes C2-chemistry [66]. For the permeable wall, the hydrogen gas flow significantly altered the flame-wall interactions with quenching occurring at a considerable distance from the wall. It was appar- ent that this was neither due to lack of oxidizer nor to heat loss to the wall and flame quenching took place before the flame heated the wall. The early quenching appeared to be a result of the mutual effects of the large local concentration of H

, reduced flame temperature and increased convective heat transfer away from the wall and flame. When the flame approached the wall and the increasing H

concentration, OH accumulation was reduced before other species (but O

) were affected. After quenching, some modest reaction heat release still took place near the wall, and this gave a peak wall

22

heat flux a while after the quenching instance, although much less than for the impermeable wall. The discussion of quenching definitions showed that some are applicable to the PW case. The flame quenching instance was based on the OH gradient in the present study [67]. Also, definitions based on maximum reaction heat release and of the minimum flame thickness ap- peared applicable. On the other hand, the definition based on maximum wall heat flux failed to capture the cease of major reaction heat release.

3.1.4 Article 4

Title: Local entropy generation and entropy fluxes of a transient flame dur- ing head-on quenching towards solid and hydrogen-permeable porous walls Co-Author: Ivar S. Ertesv˚ ag

This paper presents further investigations of article 1 and 2 on 1-d HOQ premixed H

-air flame interacting with an impermeable wall (IW) or a per- meable wall (PW) on the computation of local entropy generation and en- tropy fluxes. The calculation of entropy components was performed through solving post-processing subroutines in S3D code with the detailed chemical mechanism of 19 elementary reactions to identify major reactions contribu- tion to entropy during flame quenching process [68]. The aim of the present study understands near-wall irreversibilities during the HOQ process.

Fuel permeation through the wall aid to increase both entropy generation and fuel conversion. The fuel permeation fuel had a diversity of effects near- wall region. First, it had a cooling effect on the near-wall region. Separately, thermal dilution subsides the local temperature and contribute to increased entropy generation. However, for initially lean and stoichiometric mixtures, the additional fuel provided more reaction heat release, leading to a higher temperature and reduced entropy generation per unit of converted fuel.

Permeation also increased the mass flux, and thereby the entropy flux, away from the wall. The effects of mass diffusion on entropy generation were

23

modest, and the altered mass diffusion made small changes from IW to PW.

The Soret diffusion (thermodiffusion) had a small contribution to the mass diffusion entropy generation. During quenching, it became even smaller for IW, while it had an increase for PW. The effects of pressure diffusion were negligible. The effects of permeation were similar for all unburnt- temperatures investigated (750 K, 500 K, 300 K). As expected from theory and other studies, a lower temperature gave higher entropy generation.

In transient FWI entropy, the chemical reaction gave the major part of en- tropy generation, with conduction as the second most important source in accordance with previous literature. Mass diffusion was of modest impor- tance, while viscous forces were negligible effects—the reduced entropy gen- eration per unit of fuel converted to a lean mixture. The effect was stronger for lower temperatures because then the conduction had a greater share of the total entropy generation. At the higher unburnt-mixture temperature, similar results were seen for rich mixtures, as well. For the lower tempera- ture, permeation into a rich mixture increased the entropy generation per unit of converted fuel.

The elementary reactions, R8 (OH + H + M –> H

O+M, net forward), R5 (H

+ M –> 2 H + M, net reverse) and R3 (OH + H

–> H + H

O, net forward) were most important for entropy generation towards quenching.

The R5r as recombination reaction had a notable relative increase towards the flame quenching instance. High peaks of entropy generation rate of R8f and R5r observed when the flame reached the wall and quenched.

3.2 2-D side-wall quenching (SWQ) configuration

In the study of the two-dimensional configuration reported in Article 1, the laminar planar flame propagated in a channel against the approaching reac- tants flow speed. In SWQ, the flame burned parallel to the wall. Note that the flame propagated freely to either upstream or downstream, depending on flame speed relative to the approaching flow in the present setup. The

24

present study supplements Article 1 to discuss SWQ flame characteristics for an initially lean-fuel case for IW and PW. The latter led to the formation of secondary, non-premixed flame with fuel seeping through the membrane and burning with the excess oxygen from the primary premixed flame. The double-flame arrangement, consisting of a primary premixed flame and a secondary non-premixed flame was only observed in fuel-lean conditions.

The stoichiometric and rich mixture conditions did not show the double- flame arrangement, as most of available oxygen was consumed in its side-on quenching sweep of the boundary layer. This caused the additional fuel supplied by PW to accumulate near the wall.

Figure 3.2 shows the flame temperature for x

= 0.5 for lean-fuel conditions.

The non-dimensional distances to the wall are given by x

= x/L

and y

= y/L

respectively. The spatial dimensions in the two-dimensional domain were L

= 0.02 m and L

= 0.01 m for the main flow and wall- normal direction, respectively. The non-dimensional or reduced temperature is defined as T

= (T - T

)/(T

- T

), where T

is the burned mixture temperature. The reduced temperature of IW showed that the flame moved towards the outlet because no fuel was injected into the near-wall region.

The flame was convected downstream towards the outlet of the domain and blown-off by incoming fresh reactants. PW showed the opposite behaviour of flame propagating upstream of the channel at inflow boundary and reached a temperature higher than the burnt mixture temperature. Figure 3.3 shows total heat release rates for x

= 0.5 at fuel-lean conditions. The peaked magnitudes of the heat release rate at the wall were observed for IW as the flame moved towards the outlet at a different time instants. PW showed a different trend of heat release rate, with decreasing peaked magnitudes at a distance from the wall compared to IW. Both walls in 2-d SWQ setup showed low peak values of quenching heat release rate at the wall, resulting in low quenching wall heat-flux values compared to 1-d HOQ (see Article 1).

It is commonly seen that experimental SWQ setup use planar laser-induced fluorescence for tracking hydroxyl distributions (OH-PLIF) to identify the

25

0 0.05 0.1 0.15 0.2 0.25 0.3 0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

t = 0 s t = 0.1ms t = 0.2 ms t = 0.3 ms t = 0.4-1.0 ms

0 0.1 0.2 0.3 0.4 0.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

t = 0s t = 0.1 ms t = 0.2 ms t = 0.3 ms t = 0.4 ms t = 0.5 ms t = 0.6 ms t = 0.7 ms t = 0.8 ms t = 0.9 ms t = 1ms

Figure 3.2: Reduced Temperature (T

) profiles of flame at x

= 0.5 for (a) Im- permeable wall (IW) and (b) Permeable wall (PW) with hydrogen flux at lean-fuel conditions (φ =0.5).

0 0.1 0.2 0.3 0.4 0.5

0 0.5 1 1.5 2

t = 0 s t = 0.1 ms t = 0.2 ms t = 0.3 ms t = 0.4 -1.0 ms

0 0.1 0.2 0.3 0.4 0.5

0 0.5 1 1.5 2

t = 0s t = 0.1 ms t = 0.2 ms t = 0.3 ms t = 0.4 ms t = 0.5 ms t = 0.6 ms t = 0.7 ms t = 0.8 ms t = 0.9 ms t = 1 ms

Figure 3.3: Non-dimensional total heat release rate (HR) profiles of flame at x

= 0.5 for (a) Impermeable wall (IW) and (b) Permeable wall (PW) with hydrogen flux at lean-fuel conditions (φ =0.5). The HR magnitude of initialized flame away from wall is taken for normalization of HR profiles.

flame front location. Flame quenching is expressed as a wall-normal dis- tance, y

, see figure 3.4. It is defined as the flame location where the normalized spatial OH gradient fells or reaches below half of its maximum value. Here, the OH gradient is normalized by the maximum OH gradient of the initialized flame at wall-normal distance. The adopted definition for numerical simulations was taken from laser diagnostics [67, 69], where the OH molecule is used to identify the flame front. The quenching Peclet num- ber is given as Pe

= y

/δ

where δ

is characteristic flame thickness.

The definition of δ

can be found in Articles 2 and 3. The flame speed, S

26

Figure 3.4: 2-d side-wall quenching (SWQ) setup at fuel-lean condition (φ =0.5).

The quenching distance is given as y

, and the Peclet number (Pe

) is defined based on OH concentration.

0.5 0.52 0.54 0.56 0.58 0.6

2.5 3 3.5 4 4.5 5 5.5 6

Flame propagates towards downstream

t = 0s

t = 1ms

0.1 0.2 0.3 0.4 0.5 0.6

2.5 3 3.5 4 4.5 5 5.5 6

Flame propagates towards upstream

t = 1ms

t = 0s

Figure 3.5: Quenching Peclet number (Pe

) at different time instants for (a) Impermeable wall (IW) and (b) Permeable wall (PW) with hydrogen flux at lean- fuel condition (φ =0.5).

is computed from IW after initialization of the flame at x

= 0.5.

Figure 3.5 shows the different temporal evolutions of the quenching Peclet number (Pe

) after initialization. IW showed that flame quenching occurs much closer to the wall, as flame progress towards the outlet or downstream of the domain and reaches stable Pe

values around 3.2 with blow off or negative flashback velocity at 1.2 m/s. On the other hand, PW showed that flame progressed towards inflow boundary or upstream direction. The flame quenching occurred away from the wall as observed in the varying Pe

trend as time progressed. The hydrogen mass flux was primarily

27

determined by the difference of partial pressure of hydrogen at the wall and permeate sides. The hydrogen flux by PW led to an increase of the local equivalence ratio in the near-wall region. The premixed mixture changed to a stratified fuel-air mixture and propagated towards the reactants inlet at the left or upstream boundary. This led to a large flashback velocity of 5.44 m/s in the laminar channel flow configuration. The PW or novel fuel diffuser at fuel-lean conditions needs a careful designed turbulent sweep flow in the near-wall region that removes hydrogen fuel to avoid the large impact of boundary layer flashback velocities.

3.3 Discussion

Figure 3.1 outlines the pathways of articles based on flame-wall interaction (FWI) with hydrogen permeable wall boundary implemented in the S3D DNS code. The mass flux of hydrogen across the wall was based on the wall boundary formulation described in Sect. 2.2.2. PW mimics the membrane behavior of the hydrogen flow across the wall and its consumption with low- ering of its partial pressure in the combustion process. The PW provides an outline of non-zero scalar, isothermal wall boundary condition that allows a hydrogen gas flow in combustion simulation. The PW membrane related constants were kept constant for all simulations. Articles 1 and 2 are per- formed for hydrogen-air mixtures. Article 1 was a first attempt to model hydrogen injection through the wall as a porous fuel diffuser to understand near-wall flow physics during flame quenching process. The investigations were carried out for laminar flames subjected to head-on and side-wall con- figurations at different equivalence ratios. In Article 2, the investigations of the 1-d HOQ configurations were extended with effects of variations in varying wall mass flux i.e permeation pressure difference, stoichiometry, di- lution, and unburnt gas and wall temperatures. All studies provided FWI characteristics and influence of the hydrogen flow through the membrane on local wall chemistry and heat transfer. The implications of modeling was that initial lean-fuel mixture conditions with PW resulted in significant in-

28

crease of wall heat flux and large heat release rate at the wall. On the other hand, rich and stoichiometric conditions gave moderate reduction of wall heat flux due to PW boundary. The quenching instant definition based on heat release rate and wall heat flux was appropriate for premixed hydrogen based flames. Article 3 extends the study performed for methane-air mix- tures with a hydrogen permeable wall boundary. Hydrogen released through PW as a secondary fuel participated and influenced on FWI characteristics.

Different FWI characteristics were observed in comparison to hydrogen-air mixtures. The flame quenching instant based on OH gradient was more ap- propriate than the definition based on maximum reaction heat release rate and minimum flame thickness.

Article 4 is an extension of Articles 1 and 2 with the focus on local entropy production or irreversibilities and entropy fluxes computations near the wall.

In transient FWI, chemical reactions and conduction remained important sources of entropy production. The viscous effects remained negligible for all computations.

The 2-d SWQ results of Article 1 are discussed here (Sect. 3.2) related to the FWI characteristics. They showed different results of reduced temper- ature profiles (see Fig. 3.2), non-dimensional heat release rate profiles (see Fig. 3.3) and higher quenching Peclet (Pe

) in the channel flow compared to the 1-d HOQ configuration, both for IW and PW. In 1-d HOQ, the flame quenching distance occurred close to the PW wall compared to IW at fuel- lean conditions. In the SWQ setup, the flame quenching distance tends to be farther away from the PW wall due to the impact of membrane hydrogen flux compared to the convectional IW at fuel-lean conditions. The temporal Pe

trend seen in Fig. 3.5 clearly shows that IW led to stable Pe

values as the time progressed, indicating flame blow off. In contrast, the different trend of Pe

was observed for PW with the flashback velocity of 5.44 m/s in the near-wall boundary. The Pe

trend in PW was primarily dependent on hydrogen consumption in the near-wall region and the mass flux through the wall.

The novelty of the present thesis is towards the study porous fuel injection

29

systems or burners with membranes that can provide reactive hydrogen fuel flow across the wall based upon the gas diffusion characteristics of mem- brane. This study can be interesting to further work on hydrogen-based fuel design activities, both in the industry and research. Also, investigation of transient entropy generation can be performed for PW and convectional im- pervious wall (IW) boundary to understand irreversibilities during the flame quenching process. The entropy study could assist in design improvements related to near-wall losses or system performance as micro combustion.

30

Chapter 4

Conclusions and further work

4.1 Summary

Numerical simulations of laminar flame-wall interaction for hydrogen-air and methane-air flames were performed in the high-order numerical S3D DNS code. There was successful implementation of selective species H

wall boundary condition for permeable wall (PW), which satisfied well-posedness conditions. The motivation of the present work is the development of even- tual future utilization of porous wall boundary surfaces or porous fuel dif- fuser with a distributed fuel injection of reactive H

gas and thereby re- placement of traditional fuel nozzles.

The following conclusions can be drawn from the present thesis:

1. The PW or membrane boundary facilitates H

fuel supply as addi- tional fuel across the wall, based on the pressure difference between feed and permeate side. It affects near-wall radical reactions charac- terised by low-activation energies. H

permeation influences the wall heat release rate during the quenching process and exhibits different FWI characteristics in comparison to the corresponding IW cases.

2. The hydrogen flux through the wall in PW is affected by the pres-

31

ence of the propagating flame, that resulting in a strong feedback mechanism between wall surface and flame. This mechanism greatly increases boundary layer flashback velocities at lean fuel conditions in laminar SWQ configurations (see Article 1). The lean 2-d SWQ setup with PW showed reduced heat release rates and temperature profiles compared to the 1-d HOQ setup at quenching as flame prop- agated parallel to the wall. The temporal evolution of Pe

showed that flame quenching occurs farther away from the wall for PW in comparison to 1-d HOQ at fuel-lean conditions (See Sect 3.2).

3. The presence of PW showed different FWI characteristics for varying (initially) premixed flames in comparison to the corresponding IW cases for HOQ. The findings (see Articles 1 and 2) showed that (ini- tially) fuel-rich and stoichiometric flames result in reduced quenching wall heat flux in comparison to the IW cases. Conversely, an (initially) fuel-lean flame at φ

= 0.5 showed an increased quenching wall heat flux magnitude by a factor of three in comparison to the IW case.

4. The influence of the wall on the flame is felt much earlier for PW than for the corresponding IW case. The fuel permeation gives a locally richer mixture at the PW, giving more H radicals than O radicals close to the wall, resulting in a notable increase of the recombination reaction 2H→H

(Reaction R5 reverse) towards flame quenching. A lower initial temperature and diluents (N

as inert and H

O as partici- pating species) reduce the burned mixture temperature and eventually reduce the wall heat flux. With diluents, flame propagation and the quenching instance are delayed (see Article 2).

5. In premixed methane-air flame interaction with PW, flame quenching occur earlier than in the IW case, and with a considerable flame wall distance owing to mutual effects of the large concentration of H

, re- duced flame temperature and increased convective heat transfer away from the wall and flame. When the flame reaches close to the wall, increased H

concentration leads to a reduction of OH accumulation before other species (but O

) are affected. The conventional flame-

32